A MODEL FOR THE EFFECT OF A GASEOUS ENVIRONMENT ON THE LEFM FATIGUE THRESHOLD CONDITION OF STEELS

Using a different approach to those methods involving hydrogen-embrittlement and crack-closure mechanisms a previously developed model is extended to predict the commonly observed effects of yield strength and a gaseous environment on the long-crack fatigue crack growth threshold. The model assumes the existence of two intrinsic thresholds namely an upper bound value and a lower bound value related to, respectively, K_max-controlled cleavage and δK-controlled reversed shear mechanisms of crack growth in a critically stressed volume at the crack tip. This new development assumes that nascent hydrogen atoms, liberated from moisture in the environment, assist in reducing dislocation mobility thereby rationalizing experimental observations on low strength materials in moist laboratory air when compared to a dry inert environment. Quantitative predictions of fatigue thresholds in laboratory air and inert environments show good agreement with experimental data for several low and high strength steels. This alternative procedure may be found to be useful in practical design applications when reasonably fast and accurate estimates are required.     

SMALL FATIGUE CRACK GROWTH IN A LOW CARBON STEEL UNDER TENSION–COMPRESSION AND PULSATING-TENSION LOADING

The growth behaviour of small fatigue cracks has been investigated in a low carbon steel under axial loading at the stress ratios R of –1 (tension-compression) and 0 (pulsating-tension). Crack closure was measured to evaluate the effects of stress ratio and stress level on small crack growth. Except for the accelerated growth at stress levels close to the yield stress of the material, at R=–1 small cracks grow faster than large cracks below a certain crack length, but at R= 0 the crack growth rates for small cracks are coincident with those for large cracks in the whole region of crack length investigated. The critical crack length, 2c_c, above which the growth behaviour of small cracks is similar to that of large cracks depends on stress ratio, being 1–2 mm at R=–1 and smaller than 0.7 mm at R=0. The 2c_c value at R=–1 agrees with that obtained under rotating bending (R=–1). The small crack data are closely correlated with large crack growth rates in terms of the effective stress intensity range, ΔK_eff; thus ΔK_eff is found to be a characterizing parameter for small crack growth including the growth at the higher stress levels.     

Effect of prior austenite grain size and pearlite interlamellar spacing on strength and fracture toughness of a eutectoid rail steel

Abstract

The influence of prior austenite grain size d_γ, and true interlamellar spacing of pearlite S_t on the strength and fracture toughness of a eutectoid rail steel has been investigated. Specimens were machined from rail sections and heat treated to produce a wide variation in d_γ and s_t. Mechanical properties studied included 0·2% proof stress σ_0·2, ultimate tensile strength σ_u, tensile ductility δ, cleavage fracture stress σ_f, and plane strain fracture toughness K_1c. All tests were performed at a temperature of ?80°C. The values of σ_0·2 and σ_u increase as s_t decreases. The proof stress is related to the mean free distance λin the pearlitic ferrite by a Hall–Petch equation. A microstructural dependence similar to that of σ_0·2 is shown by σ_f and for all but the finest pearlites σ_f is interpreted as a shear stress controlled cleavage nucleation stress. The value of K_1c first decreases with decreasing s_t and then increases for the finest spacings. This behaviour is attributed to a change in the micromechanism of cleavage nucleation as the pearlite spacing changes from coarse to fine. The value of d_y has very little effect on K_1c, but δ decreases progressively as d_γ increases. The effect of d_γ on K_1c is negligible because the fracture process zone is much smaller than the grain size and therefore the grain boundaries cannot influence the fracture processes occurring at the crack tip. The tensile ductility is interpreted as the strain necessary to develop an internal microcrack which then propagates as a quasibrittle fracture. The size of the microcrack is shown to be related to the pearlite nodule size which in turn is related to d_γ.

MST/396     

Effects of the loadings and type of copper powder on the electrical resistivity of copper powder-polymer paint films

Conductive behaviour in copper powder-filled paint films was subdivided into three regions, I, II, and III, with copper loading. Paint films were insulators in Region I. In Region II, resistivity decreased linearly in proportion to the cube root of the volume concentration, V, of the copper powders, reaching a minimum value at a certain V, which is the critical volume concentration, V _c, of copper powders. V _c, increased linearly in proportion to the bulk density of branched copper powders. This suggests that conductivity in the region is dependent upon the packing state of the copper particles. V _c, and resistivity at V _c, decreased with decrease in the grain size of isotropic branched and spherical copper powders, although they increased for flake copper powders. In Region III, resistivity increased with increase in copper loading. The increase in resistivity was due to the decrease in the apparent density of dry paint films.     

Fracture toughness and hardness of zinc sulphide as a function of grain size

The erosion properties of brittle materials depend upon plastic deformation and crack generation at an impact or indented site. Vickers indentations have been used to investigate the plastic processes and crack systems in chemical vapour deposited zinc sulphide of different grain sizes. The hardness,H, and the local fracture toughnessK _c, are dependent upon the grain size of the material. For small grain size material (<50 m) the Vickers hardness was found to increase with decreasing grain size in accord with the Petch mechanism, i.e.H=H ₀ +kd ^–1/2 wherek andH ₀ are constants andd is the grain diameter. A maximum hardness of ca. 4 GPa has been observed for material with an average 0.5 m grain diameter. In large grain size material, hardness anisotropy within the grains causes significant experimental scatter in the hardness measurements because the plastic impression formed by the indenter (load 10 N and 100 N) is smaller than the grain diameter. The values ofK _c obtained using an indentation technique show that for grain sizes less than 8 mK _c decreases with decreasing grain size. For materials with a grain size in the range 500 m to 8 m, well developed median cracks were not observed, however, the radius of the fracture zone was measured in order to estimate an effectiveK _c. The effectiveK _c was found to increase approximately linearly with the reciprocal root of the grain size. Consideration of the models for elastic/plastic impact and micromechanics of crack nucleation in conjuction with the variation ofK _c andH, indicate that zinc sulphide with a mean grain size of 8 m will give the optimum solid particle and rain erosion resistance.     

IN SITU SEM MEASUREMENTS OF CRACK CLOSURE FOR SMALL FATIGUE CRACKS IN ALUMINIUM 2024-T351

Abstract Crack closure has been measured for a range of small, self-initiated fatigue cracks using in situ SEM loading. Cracks were grown at positive R ratios in the aluminium alloy 2024-T351 and at nominal ΔK levels that extend substantially below the corresponding long crack threshold. The crack closure stress of the small cracks decreased and the K_cl level increased with increasing crack size until the long crack value near threshold was reached. For cracks of depth larger than about one grain size, a good correlation was obtained between small and long crack growth rate data in terms of ΔK_eff     

INFLUENCE OF VARIOUS PARAMETERS ON THE DETERMINATION OF THE FATIGUE CRACK ARREST THRESHOLD Members of the Fatigue Commission of the French Metallurgical Society*

Abstract —This report presents the results of a round robin study on the fatigue crack arrest threshold (δK_th) of 2618 aluminium alloy and AISI 316 steel. The main purpose of this work was to develop a method for the determination of δK_th, and to examine the influence of various test parameters on this threshold. Among the parameters considered, only the load ratio (R) and the environment (vacuum) appear to have a significant influence on very slow fatigue crack growth rates (FCGR). Moreover, while the results obtained with the 316 steel show great scatter, the importance of the adopted procedure is pointed out.     

Influence of the cyclic plastic zone size on the propagation of the fatigue crack in case of 12NC6 steel

Under cyclic loading, the plasticized zone becomes complicated; it contains in particular a second plasticized zone, resulting from the local compression which occurs at the time of the closing of the crack to each cycle. The two plastic zones, monotonous (r_m) and cyclic (r_c), are proportional to (K_max/R_e)² et (ΔK/R_e)², respectively. The objective of this work is to study the evolution of the fatigue crack grown rate (FCGR) and the influence of the plastic zone size (r_c), which represents the seat of the residual stresses, on this evolution in the case of 12NC6 steel. Generally, the plastic zone size increases with the crack advance. The FCGR can be correlated with the energy absorptive in these plastic zones.     

FATIGUE CRACK GROWTH IN D16T A1-ALLOY SHEET SUBJECTED TO BIAXIAL OUT-OF-PHASE LOADING

Abstract— Fractographic peculiarities of fatigue crack development are studied in cruciform specimens of D16T aluminium alloy under out-of-phase biaxial tension and tension-compression. In the range of the biaxial load ratios λ from ?0.5 to +0.5 and an R-ratio of 0.3, fatigue striation formation took place beyond a crack growth rate near to 4 × 10^?8 m/cycle. The striation spacing and the crack growth rate increase as the φ-angle of the out-of-phase biaxial loads increases in the range of φ-angles from 0° to 180°. The ratio between the increment of crack growth, da/dN, and the striation spacing, δ, is approximately 1 to 1 when da/dN is greater than 4 × 10^?8 m/cycle. The relationship between the number of cycles from the beginning of a test up to the growth rate of 10^?6 m/cycle (N_d), and the crack growth period, N_P, from when the crack initiates up to the instant when that growth rate is reached, was determined for different λ ratios and φ angles. The value of N_d decreases as the φ angle is increased in the range from 0° to 1807deg;. Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method that involves an equivalent stress intensity factor K_e=K_IF₁(λ, R)F₂(φ). The values of F₂(φ) were determined. The calculated fatigue crack growth period, N_c, applicable up to and including the stage of fatigue striation formation (predicted by using both of the F₁(λ, R) and F₂(φ) functions) is correlated with the experimental data and the error is of the order of 15%.     

Sub-critical crack extension and crack resistance in polycrystalline alumina

Sub-critical crack extension can readily be observed in controlled fracture tests in fourpoint bending. A natural crack of any desired lengthc which exceeds the notch depthc ₀ by the amount c =c –c ₀ can be introduced into bend specimens by stable crack propagation. The stress intensity factor to achieve c increases considerably with increasing c. In pre-cracked specimens the stress intensity factorK _I0 to start the crack and the critical valueK _IC strongly depend on the natural crack length c whereasK _I0 andK _IC are independent ofc ₀ in solely notched specimens. From a quasi-continuous evaluation of the load-deflection curve recorded during controlled fracture, the differential work of fracture can be obtained as a function of the achieved crack length. It may be regarded as the crack extension resistanceR of the material because the balance between the energy release rateg ₁ andR is maintained throughout the experiment. By that, a formal analogy to theR-curve concept of fracture mechanics is given. The steady increase ofR is explained by multiple crack formation and by the interference of the fracture surfaces due to the angular development of the crack front.     

Determination of valid R-curves for materials with large fracture toughness to yield strength ratios

Crack growth resistance curves are derived from a generalised theory of quasi-static crack propagation due to Gurney and Hunt. Both the subcritical and continuous cracking regions are investigated, where the fracture toughness of the material may depend on the cracking rate, the reacting environment at the crack tip and the mode of fracture. Precise conditions for stability of the spreading crack relative to chosen constraints of either a displacement- or load-controlled machine are formulated. Cracking of sheet materials with high fracture toughness and low yield stress, (e.g. (K/ _y )² > 200 mm), which do not satisfy certain size requirements, is often complicated by generalised yielding at regions remote from the crack tip. Complete R-curves for such materials cannot be established with conventional testpieces in the laboratory. The present paper adopts a new experimental technique [1] where a laboratory size reinforcement rig attached to the testpiece eliminates all irreversibilities caused by generalised yielding. Valid fracture toughness values and crack growth resistance curves are thereby determined, irrespective of the amount of elastic and plastic deformations occurring at the crack tip. Successful R-curve experiments are described for fracture in a few ductile and tough materials such as 7075-T3. and 1100-0 aluminium alloys, and a low carbon steel. Comparison is made with other published R-curves, and the influence of sheet thickness and (K _1c / _y ) ratio on the geometry of R-curves is investigated. A simple relationship for R-curves is suggested, viz.: R = R ₀ + (L) ^p , where, it seems, R ₀can be identified with the plane strain toughness (i.e. R ₀ = G _1c = K _1c ² /E(1 - v ²)1/2). A possible reason for this unexpected result is given in the paper. Useful estimates of K _lcmay thus be available from thin sheet tests.Paper presented in part at the 11th Annual Meeting of the Society of Engineering Science, November 11–13, 1974, Duke University, Durham, N.C., USA.     

Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities

Crack extension paths are often irregular, producing rough fracture surfaces which have a fractal geometry. In this paper, crack tip motion along a fractal crack trace is analysed. A fractal kinking model of the crack extension path is established to describe irregular crack growth. A formula is derived to describe the effects of fractal crack propagation on the dynamic stress intensity factor and on crack velocity. The ratio of the dynamic stress intensity factor to the applied stress intensity factor K(L(D, t), V)/K(L(t), 0), is a function of apparent crack velocity V_o, microstructure parameter d/a (grain size/crack increment step length), fractal dimension D, and fractal kinking angle of crack extension path . For fractal crack propagation, the apparent (or measured) crack velocity V_o, cannot approach the Rayleigh wave speed Cr. Why V_o is significantly lower than Cr in dynamic fracture experiments can be explained by the effects of fractal crack propagation. The dynamic stress intensity factor and apparent crack velocity are strongly affected by the microstructure parameter (d/a), fractal dimension D, and fractal kinking angle of crack extension path . This is in good agreement with experimental findings.     

Plastic deformation — its role in fatigue crack propagation

Recognizing the fact that the effective driving force (ΔK _eff) determines the fatigue crack propagation (FCP) rate and that the shear strain, which is considered to develop due to an occurrence of crack closure, primarily contributes to the plastic deformation, an effort is made here to elucidate the role of plastic deformation in FCP by developing a correlation between the ΔK _eff and the applied driving force (ΔK) with shear strain as variable. The effect of the degree of plastic deformation (i.e. shear strain level) on the FCP rates at higher values of ΔK, where ΔK _eff approaches ΔK, approaching the Paris regime, appears minimal. On the other hand, the disparity between ΔK _eff and ΔK, which apparently increases with shear strain level, persists at lower values of ΔK. This suggests a strong influence of the degree of localized deformation on the FCP rates in the near threshold level. Hence, an improvement of FCP rates in the near threshold level should follow an effort that promotes the plastic deformation near the crack tip to a greater degree. This approach could, therefore, form the basis to explain the effect of the grain size, microstructure, environment,R-ratio and crack size on the near-threshold FCP rates.     

On the constancy of the specific enthalpy of fracture

The specific enthalpy of fracture due to ductile crack propagation in commercial polycarbonate sheet is calculated as ^* =A _1c/R _1c, whereA _1c is the critical energy release rate associated with the onset of unstable crack propagation andR _1c is the corresponding amount of damage (yielded material) formed per unit crack extension.A _1c andR _1c are determined from fatigue crack propagation experiments conducted at different maximum loads, load ratios and frequencies. The value of ^* obtained from all experiments is found to be 9.8±1.4 cal g^–1 (1cal = 4.184 J) which indicates that ^* is a material constant. This finding substantiates predictions of the crack layer theory.     

Grain-size dependence of Snoek peaks in niobium

The effect of grain size on the oxygen and nitrogen Snoek peaks in niobium has been studied. It has been observed that the conversion factor K given by C = K _max, where C is the concentration of oxygen or nitrogen and _max the height of the corresponding Snoek peak, is concentration independent up to about 0.06 and 0.04 wt % oxygen and nitrogen respectively.The variation of K with grain size (d) obeys the relationship K = K ₀ + k_Kd^–1/2, where K ₀ represents the value of K for an aggregate of crystals without boundaries and k _K the grain size dependence of K.     

Fracture behaviour of chemical vapour deposited and hot isostatically pressed zinc sulphide ceramics

Fracture behaviour of zinc sulphide ceramics prepared by chemical vapour deposition (CVD) followed by hot isostatic pressing (CVD + HIP) was investigated in terms of flexural strength (σ_f), plane-strain fracture toughness (K_Ic), even conditional fracture toughness (K_IQ), R-curve behaviour (variation of total fracture energy release rate, J_c with crack extension, δ/δ_c) and fracture mode. The corresponding Knoop Hardness number (KHN) and its correlations to flexural strength (σ_f) are also evaluated and reported. The present study showed that the zinc sulphide (ZnS) ceramics processed by CVD exhibited higher fracture resistance compared to ZnS processed by CVD + HIP condition. This observation is principally attributed to higher grain size associated with post-CVD HIPing process. In both conditions, the ZnS materials exhibited conditional fracture toughness (K_IQ) that decreased moderately with increased crack length due to the change in fracture mode form grossly tensile to predominant shear. A constantly rising R-curve behaviour was indicated in both the materials with significant increase in total fracture energy release rate (J_c with the normalised displacement (δ/δ_c), a parameter representing crack extension.     

FRACTOGRAPHIC ANALYSES OF FATIGUE CRACK GROWTH IN D16T ALLOY SUBJECTED TO BIAXIAL CYCLIC LOADS AT VARIOUS R-RATIOS

Abstract Fractographic peculiarities of fatigue crack development are studied in cruciform specimens of D16T aluminium alloy under biaxial tension and tension-compression. In the range of the biaxial load ratios λ from - 1 to +1.5, and in the range of R-ratios 0.05 to 0.8, fatigue striation formation took place over a crack growth rate near to 4×10^?8 m/cycle. The striation spacing and the crack growth rate decrease as the ratios λ and R increase. The ratio between the increment of crack growth, da/dN, and the striation spacing, δ, is approximately 1:1 when da/dN is greater than 4×10-^?8 m/cycle. The relationship between the number of cycles from the beginning of a test up to the growth rate of 2.14×10^?7 m/cycle (N_d), and the crack growth period, _Np, from when the crack initiates up to the instant when that growth rate is reached, was determined for different λ and R-ratios. The value of N_d increases as the stress ratio, λ, is increased. Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method involving an equivalent stress intensity factor K_e, =K₁,F(λ, R_s). The values of F(λ, R) for the growth rate (F(λ, R)_s) and for the striation spacing (F(λ, R_s) were determined and compared. The fatigue crack growth period, N^t_p, applicable to the stage of fatigue striation formation, (predicted by using both of the F(λ, R) values) is correlated with the experimental data and the error is of the order of 15%.     

Fracture surface analysis of ceramics

Flaw size, c, fracture mirror boundaries, r, fracture stress, , and critical fracture energy were measured for glasses, glass ceramics, and single and polycrystalline ceramics. The relationship r ^1/2 = constant was verified for all these materials. The mirror constants, A, in these materials were shown to be directly proportional to the average critical stress intensity factor for crack propagation, K _IC. Based on the A — K _IC relationship, the outer mirror to flaw size ratio is shown to scatter about a value of 131. Thus, the mirror constants were used to predict critical flaw sizes in these materials. The observed flaw sizes in most cases correlated well with those calculated. The cases in which poorer correlation was obtained are those in which flaw sizes were smaller than the grain size, flaws were pores or surrounded by porous regions, or where severe microcracking existed. It is shown that the elastic modulus is proportional to the mirror constant and probably to the critical fracture energy, but that the latter is highly dependent on local microstructure. The smaller inner to outer mirror ratios for polycrystalline ceramics over glasses is attributed to the difference in available paths for crack propagation.     

The influence of the stress ratio on fatigue crack growth in a cermet

The fatigue crack growth behavior in a cermet was investigated as a function of the stress ratio, R. At the higher K _max values the fracture path was through the cermet particles as well as through the binder phase. At low growth rates the fracture path was primarily through the binder phase. As a result the fatigue crack growth process, at a growth rate of l0^–7 m/cycle the rate was influenced by K _max, and to a lesser extent by the R value, whereas at a growth rate of 10^–11 m/cycle the growth rate depend upon K as well as the R value.     

Failure of brittle polymers by slow crack growth

The mechanical properties of a silica particle-filled epoxy resin composite system have been investigated in air as a function of volume fraction of particles for volume fractions ranging from 0 to 0.52. The Young's modulus and the compressive yield stress both increase as the volume fraction of silica particles is increased and various models of particle strengthening have been used to explain this behaviour. Slow crack growth in the various particulate composites has been studied using a fracture mechanics approach. The variation of crack velocity (V) with stress intensity factor (K _I) has been measured for each of the compositions investigated. In each case, a unique relationship between V and K _I has been found with K _I increasing with volume fraction of particles at a given value of V. The failure mechanisms and the variation of other fracture mechanics parameters, for example, crack opening displacement and plastic zone size with increasing particle volume fraction have been discussed.